We investigate frame theory over the binary field Z2, following work of Bodmann, Le, Reza, Tobi and Tomforde. We consider general finite dimensional vector spaces V over Z2 equipped with an (indefinite) inner product (·, ·)V which can be an arbitrary bilinear functional. We characterize precisely when two such spaces (V, (·, ·)V ) and (W, (·, ·)W ) are unitarily equivalent in the sense that the...

| Sequences of digital video images typically require vast amounts of electronic memory for storage, and occupy much bandwidth during transmission. Widely used image and video compression standards, such as JPEG and MPEG, use the two-dimensional Discrete Cosine Transform (DCT) to achieve near-optimal compression of individual frames. This is done by decomposing the the frames into components of...

We consider estimating a random vector from its measurements in a fusion frame, in presence of noise and subspace erasures. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is bounded below and above by constant multiples of the identity operator. We first consider the linear minimum mean-squared error (LMMSE) estimation of the random...

In recent years, the trend in solving optimization problems has been directed toward using heuristic algorithms such as neural networks, genetic and ant colony algorithms. The main reason for this trend can be attributed to the fact that these algorithms can be efficiently adjusted to the specific search space to which they are applied and consequently they can be used for many optimization pro...

It is well known that fluctuations of marginals high-dimensional random vectors satisfy a certain concentration estimate called the thin shell condition are approximately Gaussian. In this article we identify general on sequence under which one can exponential decay rate large deviation probabilities corresponding marginals. More precisely, consider projection an n-dimensional vector onto kn-di...